Solve (8x^9)(-3x^6)(7x^5)

$$( 8 x ^ { 9 } ) ( - 3 x ^ { 6 } ) ( 7 x ^ { 5 } )$$

Evaluate

$$-168x^{20}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and 6 to get 15.

$$8x^{15}\left(-3\right)\times 7x^{5}$$

To multiply powers of the same base, add their exponents. Add 15 and 5 to get 20.

$$8x^{20}\left(-3\right)\times 7$$

Multiply 8 and -3 to get -24.

$$-24x^{20}\times 7$$

Multiply -24 and 7 to get -168.

$$-168x^{20}$$

Differentiate w.r.t. x

$$-3360x^{19}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 9 and 6 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{15}\left(-3\right)\times 7x^{5})$$

To multiply powers of the same base, add their exponents. Add 15 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{20}\left(-3\right)\times 7)$$

Multiply 8 and -3 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-24x^{20}\times 7)$$

Multiply -24 and 7 to get -168.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-168x^{20})$$

The derivative of ax^{n} is nax^{n-1}.

$$20\left(-168\right)x^{20-1}$$

Multiply 20 times -168.

$$-3360x^{20-1}$$

Subtract 1 from 20.

$$-3360x^{19}$$